In this unit, students develop a conceptual understanding of ratios. Throughout the unit students apply this understanding to solve problems involving ratios and rates. Students’ understanding of ratios is built upon their prior work with whole number multiplication and division. In this unit students begin to shift their focus from noticing more familiar additive relationships to noticing less familiar multiplicative relationships between quantities. Students explore relationships within and between equivalent ratios and use these relationships to find missing values in ratio tables. Students then apply this thinking to measurement systems and magnitude. The work that students engage with in this unit will be an integral component of their work later in Grade 6 as they begin to work with unit rates and percent, and later as they extend this understanding to proportionality, and eventually slope.
Content Standards: 6.RP.A.1, 6.RP.A.3, 6.RP.A.3a, 6.RP.A.3d
Practice Standards: MP1, MP4, MP5
Unit at a glance
Lessons 14 (4 days)
Key Concept 1: Additive relationships are preserved by adding the same number to the quantities being compared. Multiplicative relationships are preserved by multiplying the quantities being compared by the same factor.

Lesson objective: Understand the distinction between additive comparisons and multiplicative comparisons of quantities. Ratios will be defined as a multiplicative comparison, meaning we use multiplication and division in ratio situations. Students are i...

Lesson objective: Represent a situation using a ratio, in multiple different ways. This lesson helps to build fluency with writing ratio statements. The distinction between parttopart and parttowhole relationships is used here because it supports st...

Lesson objective: Create and simplify equivalent ratios using visual models, tables, and fractions. This lesson helps to build fluency with equivalent ratios. Ratio tables are used here because it supports students' development of multiplicative relatio...

Lesson objective: Apply creating and simplifying equivalent ratios to solve a problem. This lesson provides an opportunity for students to apply their knowledge and understanding of ratio relationships to a reallife situation. Students are asked to hel...
Lessons 57 (3 days)
Key Concept 2: Equivalent ratios show the same multiplicative relationship; the "between" relationship shows that both quantities were scaled in the same way; the "within" relationship means that the ratios have the same quotient, and therefore the same unit rate.

Lesson objective: Understand that multiplicative relationships exist both between and within equivalent ratios. Students bring prior knowledge that ratios show multiplicative relationships between quantities (6.RP.A.3.a ). This prior knowledge is extend...

Lesson objective: Use multiplicative "between" and "within" relationships to find missing values in a table. This lesson helps to build fluency with finding missing values in a ratio table. Ratio tables are used here because they highlight the multiplic...

Lesson objective: Use "between" and "within" relationships in equivalent ratios in order to find missing values in a ratio table. This lesson provides an opportunity for students to apply their knowledge and understanding of ratios to a reallife situat...
Lessons 810 (3 days)
Key Concept 3: Measurement systems involve multiplicative relationships; while a magnitude is invariant, the number we use to describe the magnitude is dependent on the unit of measurement.

Lesson objective: Understand that ratios can be used to convert between units of measurement. Students bring prior knowledge of converting between units using multiplication from 4th Grade (4.MD.A.1). This prior knowledge is extended to using ratio reas...

Lesson objective: Convert measurements in one unit to another unit. This lesson helps to build fluency with measurement conversion. Ratio tables are used here because it supports the understanding that multiplicative relationships exist in measurement c...

Lesson objective: Apply conversions of measurement systems using ratio relationships to a reallife situation. This lesson provides an opportunity for students to apply their knowledge and understanding of conversions of measurement systems using relati...